# Unit Normal for Epicycloid

1. Nov 19, 2015

### bugatti79

Hi Folks,

I got stuck towards the end where it ask to derive the unit normal (eqn 3.2.29 I don't know how they arrived at $$n_x$$. I have looked at trig identities....and I have assumed the following

$$n_x=\frac{N_x}{|N_x|}$$

I dont see the (r+p) term anywhere in neither the top nor bottom.

PS: I have posted this in MHB on Tues but no response.
http://mathhelpboards.com/calculus-10/unit-normal-epicycloid-16922.html

Thanks

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2. Nov 19, 2015

### fzero

The norm of the normal vector is $|\mathbf{N}| = \sqrt{ N_x^2 + N_y^2 }$. The unit normal is $\mathbf{n} = \mathbf{N}/ |\mathbf{N}|$, so
$$n_x = \frac{ N_x}{\sqrt{N_x^2 + N_y^2}}.$$
In particular, there are common factors of $r+\rho$ in the numerator and denominator that cancel out. The rest of the simplification of the denominator can be accomplished with some trig identities.

3. Nov 20, 2015

### bugatti79

Ok, great thanks. I should work it out now.